The solution was found very quickly, by everyone, including Lucian and Zephyr. Naturally, they argued about it.

Thomas: That was fairly easy.

Hale: But we get your point.

Rachel: Yeah, sometimes the doubled pawn gives you an extra tempo.

Professor: I think it's time for another problem.

Question 2: Can White force mate in four moves?

The class dispensed with this one expeditiously. It left time for some good-natured camaraderie.

Rachel: The extra rook-pawn truly did help out.

Thomas: It gave a vital tempo.

Hale: And it delivered the death blow.

Professor: Let's try another problem.

Question 3: Can White force a win?

This problem proved a little harder, but careful work, even amid the contention, produced a viable answer.

Lucian: That was a little tricky.

Zephyr: Maybe for you.

Idris: Maybe for all of us.

Hale: Yet it was different.

Ryan: True. In several lines, the doubled pawn guarded an important square.

Rachel: But Professor, surely such a pawn complex doesn't always win.

Professor: No, of course not. Sometimes it only helps us draw.

Lucian: May we see the next problem?

Professor: You may.

Question 4: Can White force a draw?

A couple of small dance steps and the group had the answer. There were some comments, too.

Rachel: So the extra rook-pawn was a useful obstruction.

Thomas: But certainly doubled isolated pawns can be very bad.

Professor: How about a problem where they're bad for an unexpected reason?

Lucian: Can we see it?

Professor: Absolutely, courtesy of Botvinnik, who once published a version of it.

Question 5: Can White force a win?

The problem was solved and the class had a good laugh. It was time for reevaluation.

Ryan: I guess that was a Botvinnikian joke.

Idris: It's funny. Black loses because he has too many rook-pawns.

Rachel: Especially the one at a6.

Hale: I love Botvinnik's humor.

Lucian: You're not seriously suggesting that doubled isolated rook-pawns are an advantage.

Zephyr: Or that Botvinnik's sense of humor was actually funny?

Professor: No I'm not trying to imply any of that, though I did like Botvinnik's sense of humor.

Zephyr: So you agree that generally doubled isolated rook-pawns do not constitute an advantage.

Professor: Not in the best of all possible worlds.

Zephyr: That's good to hear, Doctor Pangloss. I mean, Professor.

Answers below -- Try to solve NM Pandolfini's puzzles first!

Answer 1: White wins by 1. Nf6. Here the knight attacks the bishop and eyes both e8 and d5, which are transfer points to c7. If Black defends with 1...Bf7, White's a5-pawn grants a tempo, 2. a6, and mate can't be stopped. Black could then try 2...Bd5 (hoping for 3. Nxd5??, stalemate), but 3. Ne8 mates next move.

To be sure, doubled isolated rook-pawns are usually very undesirable. But not always. Part of the problem stems from when we first learn about them. As young players, we're told over and over to avoid them, almost without exception.

That emphasis can be debilitating and counterproductive. It can lead to atrophy of the mind. Like practically everything else, such elements (doubled isolated rook-pawns) must be evaluated in specific context.

Certainly, chess requires a good deal of general thinking, but if we think too generally, we may wind up not thinking at all.